32 research outputs found
Principal Portfolios: Recasting the Efficient Frontier
A new method of analyzing the efficient portfolio problem under the assumption that short sales are allowed is presented. It is based on the remarkable finding that the original asset set can be reorganized as a set of uncorrelated portfolios, here named principal portfolios. The original problem of portfolio selection from the existing, correlated assets is thereby traded for the reduced problem of choosing from a set of uncorrelated portfolios. These portfolios constitute a new investment environment of uncorrelated assets, thereby providing significant conceptual and practical simplification in any portfolio optimization process such as the determination of the efficient frontier. The principal portfolio analysis of the efficient frontier reveals new features of the volatility structure of the optimal portfolios.
Reexamination of the A-J effect
We establish four necessary and sufficient conditions for the existence of the Averch-Johnson effect in a generalized version of their famous model of the rate-of-return regulated firm. The four necessary and sufficient conditions are then compared to the two stronger sufficient conditions for the Averch-Johnson effect found in the literature. Our analysis also permits us to put to rest a somewhat protracted debate about the very existence of the Averch-Johnson effect.
Correlative Capacity of Composite Quantum States
We characterize the optimal correlative capacity of entangled, separable, and
classically correlated states. Introducing the notions of the infimum and
supremum within majorization theory, we construct the least disordered
separable state compatible with a set of marginals. The maximum separable
correlation information supportable by the marginals of a multi-qubit pure
state is shown to be an LOCC monotone. The least disordered composite of a pair
of qubits is found for the above classes, with classically correlated states
defined as diagonal in the product of marginal bases.Comment: 4 pages, 1 figur
Hamilton-Jacobi Formulation of KS Entropy for Classical and Quantum Dynamics
A Hamilton-Jacobi formulation of the Lyapunov spectrum and KS entropy is
developed. It is numerically efficient and reveals a close relation between the
KS invariant and the classical action. This formulation is extended to the
quantum domain using the Madelung-Bohm orbits associated with the Schroedinger
equation. The resulting quantum KS invariant for a given orbit equals the mean
decay rate of the probability density along the orbit, while its ensemble
average measures the mean growth rate of configuration-space information for
the quantum system.Comment: preprint, 8 pages (revtex
Electrodynamics of a Magnet Moving through a Conducting Pipe
The popular demonstration involving a permanent magnet falling through a
conducting pipe is treated as an axially symmetric boundary value problem.
Specifically, Maxwell's equations are solved for an axially symmetric magnet
moving coaxially inside an infinitely long, conducting cylindrical shell of
arbitrary thickness at nonrelativistic speeds. Analytic solutions for the
fields are developed and used to derive the resulting drag force acting on the
magnet in integral form. This treatment represents a significant improvement
over existing models which idealize the problem as a point dipole moving slowly
inside a pipe of negligible thickness. It also provides a rigorous study of
eddy currents under a broad range of conditions, and can be used for precision
magnetic braking applications. The case of a uniformly magnetized cylindrical
magnet is considered in detail, and a comprehensive analytical and numerical
study of the properties of the drag force is presented for this geometry.
Various limiting cases of interest involving the shape and speed of the magnet
and the full range of conductivity and magnetic behavior of the pipe material
are investigated and corresponding asymptotic formulas are developed.Comment: 20 pages, 3 figures; computer program posted to
http://www.csus.edu/indiv/p/partovimh/magpipedrag.nb Submitted to the
Canadian Journal of Physic